So currently, the recently-reinstated My Pokédex shows all Pokémon that you've had in the past. My first suggestion is this:

Either edit this page, or create a new one called My Collection, to do a similar job, but that only shows uniques that you currently have.

Linked into this, I see there's a % completion rate. So in response to that:

Create new achievements, such as 1% completion, 5% completion, 10% completion, 25% completion and so on. Rewards could be things like special alternate forms of otherwise unobtainable Pokémon. For example, 1% could be a Shiny Non-A Unown, 5% could be a random non-special Rotom form, 10% a random Arceus form, and 25% a random special Giratina (Origin). Note: This would work best with the My Collection idea above.

Adding to this, there's the option of having to have 1%, 10%, 25% etc. be originally owned for an added challenge.

And now a more minor suggestion:

Giratina (Origin) is on the list, yet only currently available as a Golden. Perhaps add all others in this situation (Therian forms, Keldeo Resolute etc.) to the Pokédex so that they count too?

Create new achievements, such as 1% completion, 5% completion, 10% completion, 25% completion and so on. Rewards could be things like special alternate forms of otherwise unobtainable Pokémon. For example, 1% could be a Shiny Non-A Unown, 5% could be a random non-special Rotom form, 10% a random Arceus form, and 25% a random special Giratina (Origin). Note: This would work best with the My Collection idea above.

Adding to this, there's the option of having to have 1%, 10%, 25% etc. be originally owned for an added challenge.